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Algebra 2 Chapter 1.1-1.2
Class Objectives
Review:
Solving Equations
order of operations
Chapter 1.1-1.2
Graph real numbers on a number line
EXAMPLE 1
Graph the real numbers – 5 and 3 on a number line.
4
SOLUTION
5
Note that – = –1.25. Use a calculator to approximate
4
3 to the nearest tenth:
3
1.7. (The symbol means is approximately
equal to.)
5
So, graph –
between –2 and –1, and graph 3 between
4
1 and 2, as shown on the number line below.
GUIDED PRACTICE
1.
for Examples 1 and 2
7
Graph the numbers – 0.2,
10
, –1, 2 , and – 4 on a number line.
ANSWER
–4
–4
–1 – 0.2
–3
–2
–1
0
7
10
2
1
2
3
4
Chapter 1.1-1.2
Identify properties of real numbers
EXAMPLE 3
Identify the property that the statement illustrates.
a.
7+4=4+7
SOLUTION
b.
13
Commutative property of addition
1
13
SOLUTION
= 1
Inverse property of multiplication
for Examples 3 and 4
GUIDED PRACTICE
Identify the property that the statement illustrates.
3.
(2
SOLUTION
4.
3) 9 = 2
(3
9)
Associative property of multiplication.
15 + 0 = 15
SOLUTION
Identity property of addition.
GUIDED PRACTICE
for Examples 3 and 4
Identify the property that the statement illustrates.
4(5 + 25) = 4(5) + 4(25)
5.
SOLUTION
6.
1
Distributive property.
500 = 500
SOLUTION
Identity property of multiplication.
Chapter 1.1-1.2
Chapter 1.1-1.2
Chapter 1.1-1.2
EXAMPLE 4
a.
b.
c.
8x + 3x
Simplify by combining like terms
= (8 + 3)x
Distributive property
= 11x
Add coefficients.
5p2 + p – 2p2
= (5p2 – 2p2) + p
Group like terms.
= 3p2 + p
Combine like terms.
3(y + 2) – 4(y – 7)
= 3y + 6 – 4y + 28
= (3y – 4y) + (6 + 28)
= –y + 34
Distributive property
Group like terms.
Combine like terms.
GUIDED PRACTICE
8.
for Example 5
Identify the terms, coefficients, like terms, and
constant terms in the expression 2 + 5x – 6x2 + 7x – 3.
Then simplify the expression.
SOLUTION
Terms:
2, 5x, –6x2 , 7x, –3
Coefficients:
5 from 5x, –6 from –6x2 , 7 from 7x
Like terms:
5x and 7x, 2 and –3
Constants:
2 and –3
Simplify:
–6x2 +12x – 1
GUIDED PRACTICE
13.
8(x – 3) – 2(x + 6)
SOLUTION
6x – 36
14.
–4y – x + 10x + y
SOLUTION
9x –3y
for Example 5
EXAMPLE 5
Simplify a mathematical model
Digital Photo Printing
You send 15 digital images to a printing
service that charges $.80 per print in
large format and $.20 per print in small
format. Write and simplify an
expression that represents the total
cost if n of the 15 prints are in large
format. Then find the total cost if 5 of
the 15 prints are in large format.
EXAMPLE 1
Evaluate powers
a.
(–5)4 = (–5)
b.
–54 = –(5
5
(–5)
5
(–5)
5)
(–5)
= –625
= 625
EXAMPLE 2
Evaluate an algebraic expression
Evaluate –4x2 – 6x + 11 when x = –3.
–4x2 – 6x + 11
= –4(–3)2 – 6(–3) + 11
Substitute –3 for x.
= –4(9) – 6(–3) + 11
Evaluate power.
= –36 + 18 + 11
Multiply.
= –7
Add.
GUIDED PRACTICE
5.
3y2 – 4y when y = – 2
SOLUTION
20
6.
(z + 3)3 when z = 1
SOLUTION
64
for Examples 1, 2, and 3
Chapter 1.1-1.2
Home work Page 16
Quiz for lesson 1.1-1.2
1-13
Algebra 2 Chapter 1